A simple model of optimal clearance of improvised explosive devices

Motivated by experiences of coalition military forces in Iraq and Afghanistan, we analyze the allocation of route clearance teams (RCTs) to search for and neutralize improvised explosive devices (IEDs) on roadways traveled by military convoys. We model the interaction of a single RCT and a single convoy operating over a given roadway. Our goal is to reduce IED risk by improving coordination between the RCT and the convoy. We treat the distribution of IEDs along the road prior to the passage of the RCT as a non-homogeneous Poisson process. The RCT finds and clears IEDs according to a Bernoulli process. Enemy forces may emplace (reseed) additional IEDs in the temporal gap between the RCT clearance sweep and the arrival of the convoy. IED risk is defined as the expected number of IEDs encountered by the convoy. We identify certain characteristics of optimal RCT schedules including: the shape of the IED intensity function and the speed of reseeding substantially dictate the RCT schedule that minimizes IED risk; the more rapid the IED reseeding, the more critical is conformance to the optimal RCT schedule; an RCT having inferior detection probability, by employing superior scheduling can sometimes reduce convoy risk more than a less well scheduled RCT with superior detection probability; a discretized highway version of the problem can be efficiently optimized. We also briefly discuss applications of this model to the more complex problem of allocating several RCTs to protect a number of convoys scheduled to travel on a network of highways.